The generator matrix

 1  0  1  1  1  1  1  1  1  X  1  1  1  1 aX  1  1  1  1 (a+1)X  1  1  1  1  0  1  1  1  1  X  1  1  1  1 aX  1  1  1  1 (a+1)X  1  1  1  1  1  1  1  1  1  0  1  X  1  1 aX  1  1
 0  1 (a+1)X+1  a (a+1)X+a+1  X aX+1 X+a aX+a+1  1 aX X+1 aX+a X+a+1  1 (a+1)X  1 (a+1)X+a a+1  1  0 (a+1)X+1  a (a+1)X+a+1  1  X aX+1 X+a aX+a+1  1 aX X+1 aX+a X+a+1  1 (a+1)X  1 (a+1)X+a a+1  1  0  X (a+1)X+1 aX+1 aX X+1  a X+a (a+1)X+a+1  1 aX+a+1  1 aX+a X+a+1  1 (a+1)X  1

generates a code of length 57 over F4[X,sigma]/(X^2) who´s minimum homogenous weight is 170.

Homogenous weight enumerator: w(x)=1x^0+108x^170+96x^171+36x^174+6x^180+9x^184

The gray image is a linear code over GF(4) with n=228, k=4 and d=170.
This code was found by Heurico 1.16 in 0.015 seconds.